"Using Triangle Congruence to Measure Distance" Triangle PPT Courseware

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"Using Triangle Congruence to Measure Distance" Triangle PPT Courseware

As shown in the picture, two points A and B are located at two ends of a pond respectively. Xiao Ming wanted to use a rope to measure the distance between A and B, but the rope was not long enough. An uncle helped him come up with an idea: first pick one on the ground to directly Arrive at point C of point A and point B, connect AC and extend to D, so that CD=AC; connect BC and extend to E, make CE=CB, connect DE and measure its length, the length of DE is A, B distance between. Can you explain why? Please write down your thoughts. Solution: In △ABC and △DEC

AC=DC (known)

∠ACB=∠DCE (the vertex angles are equal)

BC=EC (known)

△ABC≌ △DEC (SAS)

AB=DE (corresponding sides of congruent triangles are equal)

In △ABD and △CBD,

∠ADB= ∠CDB

BD=BD

∠ABD= ∠CBD

∴△ABD≌△CBD

∴AB=BC

The purpose of using congruent triangles to measure distances is to change unmeasurable distances into measurable distances.

Basis: properties of congruent triangles.

Key: Construct congruent triangles.

give it a try

It is known that two points A and B are separated by a pond. The distance between A and B cannot be directly measured. Please give a suitable and feasible solution, draw a design drawing, and explain the basis.

Solution:

First, pick a point C on the ground that can directly reach point A and point B.

Connect AC and extend to D so that CD=AC;

Connect BC and extend to E so that CE=CB,

Connect DE and measure its length,

The length of DE is the distance between A and B.

Do it. There is a part as shown in the picture, but its design drawing is missing. Now I want to know the length of AB. What can you do?

1. As shown in the figure, to measure the distance between two opposite points A and B on both sides of the river, first take two points C and D on the vertical line BF of AB, so that CD = BC, and then determine the vertical line DE of BF. It can be proved that △ EDC≌△ABC, we get ED=AB. Therefore, the measured length of ED is the length of AB. The reason for determining △EDC≌△ABC is ( )

A.SSS B.ASA C.AAS D.SAS

2. There are two points A and B at the foot of the mountain. The distance between points A and B needs to be measured. Pick a point O on the ground that can directly reach points A and B, connect AO and extend it to C, so that AO=CO; connect BO and extend it to D, make BO=DO, and connect CD. It can be proved that △ABO≌△CDO, and CD=AB. Therefore, the measured length of CD is the length of AB. The reason for determining △ABO≌△CDO is ( )

A.SSS B.ASA C.AAS D.SAS

Class summary

1. Knowledge:

The purpose of using congruent triangles to measure distances is to change unmeasurable distances into measurable distances.

Basis: properties of congruent triangles.

Key: Construct congruent triangles.

2. Methods: (1) Construct congruent triangles using the extension method; (2) Construct congruent triangles using the perpendicular method.

3. Mathematical thinking: Establish the idea of ​​using congruent triangles to construct mathematical models to solve practical problems.

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For more information about the PPT courseware "Measuring the Distance of Triangles Using Triangle Congruences", please click the "Measuring Distances of Triangles Using Triangles Congruent PPT" ppt tag.

"Using Triangle Congruence to Measure Distance" Triangle PPT Courseware 4:

"Using Triangle Congruence to Measure Distances" Triangle PPT Courseware 4 Review: 1. What are the methods for determining that two triangles are congruent? 2. As shown in the figure, it is known that AO=CO and BO=DO. Prove: △ABO and △CDO are congruent. Prove: In △ABO and △CDO, AO=CO AOB= COD B..

"Using Triangle Congruence to Measure Distances" Triangle PPT Courseware 3:

"Using Triangle Congruence to Measure Distances" Triangle PPT Courseware 3 1. Review old knowledge 1. What are the necessary conditions to prove that two triangles are congruent? (1) SSS: Two triangles whose three sides are equal are congruent. (2) ASA: Two angles and their included sides are equal.

"Measuring Distance Using Triangle Congruence" Triangle PPT Courseware 2:

"Using Triangle Congruence to Measure Distances" Triangle PPT Courseware 2 Review old knowledge 1. What are the necessary conditions to prove that two triangles are congruent? (1) SSS: Three sides correspond to two equal triangles that are congruent. (2) ASA: Two angles and their included sides correspond to two equal triangles..

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Update Time: 2024-09-15

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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